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PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)

Author

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  • J. G. L'opez-Salas
  • S. P'erez-Rodr'iguez
  • C. V'azquez

Abstract

In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in \cite{lyashenkoMercurio:Mar2019} to model the dynamics of the Risk Free Rates (RFRs) that are replacing the traditional IBOR rates in the financial industry. Moreover, for the numerical solution of the proposed PDEs formulation, we develop some adaptations of the finite differences methods developed in \cite{LopezPerezVazquez:sisc} that are very suitable to treat the presence of spatial mixed derivatives. This work is the first article in the literature where PDE methods are used to value RFR derivatives. Additionally, Monte Carlo-based methods will be designed and the results are compared with those obtained by the numerical solution of PDEs.

Suggested Citation

  • J. G. L'opez-Salas & S. P'erez-Rodr'iguez & C. V'azquez, 2024. "PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)," Papers 2408.02289, arXiv.org.
    • Handle: RePEc:arx:papers:2408.02289
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    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
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    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    4. Xing Huan & Gary John Previts & Antonio Parbonetti, 2023. "Understanding the LIBOR scandal: the historical, the ethical, and the technological," Journal of Banking Regulation, Palgrave Macmillan, vol. 24(4), pages 403-419, December.
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